Average Error: 0.0 → 0.0
Time: 27.9s
Precision: 64
\[x + \left(y - x\right) \cdot z\]
↓
\[\left(y \cdot z + x\right) - x \cdot z\]
x + \left(y - x\right) \cdot z
↓
\left(y \cdot z + x\right) - x \cdot z
double f(double x, double y, double z) {
        double r21176540 = x;
        double r21176541 = y;
        double r21176542 = r21176541 - r21176540;
        double r21176543 = z;
        double r21176544 = r21176542 * r21176543;
        double r21176545 = r21176540 + r21176544;
        return r21176545;
}
↓
double f(double x, double y, double z) {
        double r21176546 = y;
        double r21176547 = z;
        double r21176548 = r21176546 * r21176547;
        double r21176549 = x;
        double r21176550 = r21176548 + r21176549;
        double r21176551 = r21176549 * r21176547;
        double r21176552 = r21176550 - r21176551;
        return r21176552;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x + \left(y - x\right) \cdot z\]
  2. Using strategy rm

  3. Applied flip-+27.9

    \[\leadsto \color{blue}{\frac{x \cdot x - \left(\left(y - x\right) \cdot z\right) \cdot \left(\left(y - x\right) \cdot z\right)}{x - \left(y - x\right) \cdot z}}\]

  4. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(x + z \cdot y\right) - x \cdot z}\]

  5. Final simplification0.0

    \[\leadsto \left(y \cdot z + x\right) - x \cdot z\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  (+ x (* (- y x) z)))